kman wrote:
Is m + z > 0?
(1) m - 3z > 0
(2) 4z - m > 0
Target question: Is m + z > 0? Statement 1: m - 3z > 0 There are several values of m and z that satisfy statement 1. Here are two:
Case a: m = 10 and z = 1. In this case, the answer to the target question is
YES, m + n is greater than zeroCase b: m = 1 and z = -2. In this case, the answer to the target question is
NO, m + n is not greater than zeroSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 4z - m > 0There are several values of m and z that satisfy statement 2. Here are two:
Case a: m = 1 and z = 1. In this case, the answer to the target question is
YES, m + n is greater than zeroCase b: m = -5 and z = 1. In this case, the answer to the target question is
NO, m + n is not greater than zeroSince we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that m - 3z > 0
Statement 2 tells us that 4z - m > 0
To make things clearer, let's rearrange the terms in the first inequality to get:
-3z + m > 0
4z - m > 0Since the inequality symbols are facing the SAME direction, we can ADD the inequalities to get:
z > 0Perfect! We now know that
z is positive, but we still need information about the value of m.
There are several ways to accomplish this. My approach is to take the system:
-3z + m > 0
4z - m > 0Multiply both sides of the top inequality by 4, and multiply both sides of the bottom inequality by 3 to get the following equivalent system:
-12z + 4m > 0
12z - 3m > 0Since the inequality symbols are facing the SAME direction, we can ADD the inequalities to get:
m > 0We now know that
m and z are both positive, which means
m + z > 0Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
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